Is it okay to put "cannot" in a present perfect tense?

Is it okay to say "we cannot have achieved this without the participation of your company.

We cannot have achieved this without the participation of your company.

This is grammatically incorrect. You should, instead, say:

We could not have achieved this without the participation of your company.

... since the action of "achieving" here seems to be something that happened in the past. This is said as something like a "Thank you. We couldn't have done it without you." which is thanking someone.

If you want to persuade rather than thank "your company", you should say:

We cannot/can't achieve this without the participation of your company.